scholarly journals Stochastic isotropic hyperelastic materials: constitutive calibration and model selection

2018 ◽  
Vol 474 (2211) ◽  
pp. 20170858 ◽  
Author(s):  
L. Angela Mihai ◽  
Thomas E. Woolley ◽  
Alain Goriely
Keyword(s):  
Model Selection ◽  
Finite Elasticity ◽  
Experimental Tests ◽  
Mechanical Tests ◽  
Large Strains ◽  
Intrinsic Variability ◽  
Mean Values ◽  
Practical Applications ◽  
Hyperelastic Materials ◽  
Hyperelastic Models

Biological and synthetic materials often exhibit intrinsic variability in their elastic responses under large strains, owing to microstructural inhomogeneity or when elastic data are extracted from viscoelastic mechanical tests. For these materials, although hyperelastic models calibrated to mean data are useful, stochastic representations accounting also for data dispersion carry extra information about the variability of material properties found in practical applications. We combine finite elasticity and information theories to construct homogeneous isotropic hyperelastic models with random field parameters calibrated to discrete mean values and standard deviations of either the stress–strain function or the nonlinear shear modulus, which is a function of the deformation, estimated from experimental tests. These quantities can take on different values, corresponding to possible outcomes of the experiments. As multiple models can be derived that adequately represent the observed phenomena, we apply Occam’s razor by providing an explicit criterion for model selection based on Bayesian statistics. We then employ this criterion to select a model among competing models calibrated to experimental data for rubber and brain tissue under single or multiaxial loads.

scholarly journals How to characterize a nonlinear elastic material? A review on nonlinear constitutive parameters in isotropic finite elasticity

2017 ◽  
Vol 473 (2207) ◽  
pp. 20170607 ◽  
Author(s):  
L. Angela Mihai ◽  
Alain Goriely
Keyword(s):  
Elastic Material ◽  
Mechanical Response ◽  
Finite Elasticity ◽  
Experimental Tests ◽  
Elastic Parameter ◽  
Hyperelastic Materials ◽  
Poisson Function ◽  
Elastic Responses ◽  
Nonlinear Elastic ◽  
Constitutive Parameters

The mechanical response of a homogeneous isotropic linearly elastic material can be fully characterized by two physical constants, the Young’s modulus and the Poisson’s ratio, which can be derived by simple tensile experiments. Any other linear elastic parameter can be obtained from these two constants. By contrast, the physical responses of nonlinear elastic materials are generally described by parameters which are scalar functions of the deformation, and their particular choice is not always clear. Here, we review in a unified theoretical framework several nonlinear constitutive parameters, including the stretch modulus, the shear modulus and the Poisson function, that are defined for homogeneous isotropic hyperelastic materials and are measurable under axial or shear experimental tests. These parameters represent changes in the material properties as the deformation progresses, and can be identified with their linear equivalent when the deformations are small. Universal relations between certain of these parameters are further established, and then used to quantify nonlinear elastic responses in several hyperelastic models for rubber, soft tissue and foams. The general parameters identified here can also be viewed as a flexible basis for coupling elastic responses in multi-scale processes, where an open challenge is the transfer of meaningful information between scales.

An Alternative Technique to Evaluate Crack Propagation Path in Hyperelastic Materials

2012 ◽  
Vol 40 (1) ◽  
pp. 42-58 ◽  
Author(s):  
R. R. M. Ozelo ◽  
P. Sollero ◽  
A. L. A. Costa
Keyword(s):  
Constitutive Model ◽  
Crack Propagation ◽  
Experimental Tests ◽  
Growth Direction ◽  
Propagation Path ◽  
J Integral ◽  
Alternative Technique ◽  
Crack Propagation Path ◽  
Hyperelastic Materials ◽  
Material Constitutive Model

Abstract REFERENCE: R. R. M. Ozelo, P. Sollero, and A. L. A. Costa, “An Alternative Technique to Evaluate Crack Propagation Path in Hyperelastic Materials,” Tire Science and Technology, TSTCA, Vol. 40, No. 1, January–March 2012, pp. 42–58. ABSTRACT: The analysis of crack propagation in tires aims to provide safety and reliable life prediction. Tire materials are usually nonlinear and present a hyperelastic behavior. Therefore, the use of nonlinear fracture mechanics theory and a hyperelastic material constitutive model are necessary. The material constitutive model used in this work is the Mooney–Rivlin. There are many techniques available to evaluate the crack propagation path in linear elastic materials and estimate the growth direction. However, most of these techniques are not applicable to hyperelastic materials. This paper presents an alternative technique for modeling crack propagation in hyperelastic materials, based in the J-Integral, to evaluate the crack path. The J-Integral is an energy-based parameter and is applicable to nonlinear materials. The technique was applied using abaqus software and compared to experimental tests.

scholarly journals Safe option-critic: learning safety in the option-critic architecture

2021 ◽  
Vol 36 ◽  
Author(s):  
Arushi Jain ◽  
Khimya Khetarpal ◽  
Doina Precup
Keyword(s):  
Model Uncertainty ◽  
Gradient Algorithm ◽  
Intrinsic Variability ◽  
Expected Return ◽  
Practical Applications ◽  
Hierarchical Reinforcement Learning ◽  
Continuous State ◽  
End Conditions ◽  
Policy Gradient ◽  
High Uncertainty

Abstract Designing hierarchical reinforcement learning algorithms that exhibit safe behaviour is not only vital for practical applications but also facilitates a better understanding of an agent’s decisions. We tackle this problem in the options framework (Sutton, Precup & Singh, 1999), a particular way to specify temporally abstract actions which allow an agent to use sub-policies with start and end conditions. We consider a behaviour as safe that avoids regions of state space with high uncertainty in the outcomes of actions. We propose an optimization objective that learns safe options by encouraging the agent to visit states with higher behavioural consistency. The proposed objective results in a trade-off between maximizing the standard expected return and minimizing the effect of model uncertainty in the return. We propose a policy gradient algorithm to optimize the constrained objective function. We examine the quantitative and qualitative behaviours of the proposed approach in a tabular grid world, continuous-state puddle world, and three games from the Arcade Learning Environment: Ms. Pacman, Amidar, and Q*Bert. Our approach achieves a reduction in the variance of return, boosts performance in environments with intrinsic variability in the reward structure, and compares favourably both with primitive actions and with risk-neutral options.

scholarly journals An Effective Method of Modeling the Deformation Behavior of Polymer Sandwich Structures with Adhesive Joints

2021 ◽  
Author(s):  
László Takács ◽  
Ferenc Szabó
Keyword(s):  
Deformation Behavior ◽  
Sandwich Structures ◽  
Experimental Tests ◽  
Mechanical Tests ◽  
Adhesive Joints ◽  
Core Material ◽  
Full Vehicle ◽  
Novel Approach ◽  
Stiffness Matrices ◽  
Layered Shells

AbstractPolymer sandwich structures have high bending stiffness and strength and also low weight. Therefore, they are widely used in the transportation industry. In the conceptual design phase, it is essential to have a method to model the mechanical behavior of the sandwich and its adhesive joints accurately in full-vehicle scale to investigate different structure partitioning strategies. In this paper, a novel approach using finite element modeling is introduced. The sandwich panels are modeled with layered shells and the joint lines with general stiffness matrices. Stiffness parameters of the face-sheets and the core material are obtained via mechanical tests. Stiffness parameters of the joints are determined by using the method of Design of Experiments, where detailed sub-models of the joints serve as a reference. These models are validated with experimental tests of glass-fiber reinforced vinyl ester matrix composite sandwich structure with a foam core. By using two joint designs and three reference geometries, it is shown that the method is suitable to describe the deformation behavior in a full-vehicle scale with sufficient accuracy.

Topics in Finite Elasticity: Hyperelasticity of Rubber, Elastomers, and Biological Tissues—With Examples

1987 ◽  
Vol 40 (12) ◽  
pp. 1699-1734 ◽  
Author(s):  
Millard F. Beatty
Keyword(s):  
Constitutive Equations ◽  
Mechanical Energy ◽  
Finite Elasticity ◽  
Physical Nature ◽  
Decomposition Theorem ◽  
Elastic Stability ◽  
Biological Tissues ◽  
Field Equations ◽  
Energy Principle ◽  
Hyperelastic Materials

This is an introductory survey of some selected topics in finite elasticity. Virtually no previous experience with the subject is assumed. The kinematics of finite deformation is characterized by the polar decomposition theorem. Euler’s laws of balance and the local field equations of continuum mechanics are described. The general constitutive equation of hyperelasticity theory is deduced from a mechanical energy principle; and the implications of frame invariance and of material symmetry are presented. This leads to constitutive equations for compressible and incompressible, isotropic hyperelastic materials. Constitutive equations studied in experiments by Rivlin and Saunders (1951) for incompressible rubber materials and by Blatz and Ko (1962) for certain compressible elastomers are derived; and an equation characteristic of a class of biological tissues studied in primary experiments by Fung (1967) is discussed. Sample applications are presented for these materials. A balloon inflation experiment is described, and the physical nature of the inflation phenomenon is examined analytically in detail. Results for the different materials are compared. Two major problems of finite elasticity theory are discussed. Some results concerning Ericksen’s problem on controllable deformations possible in every isotropic hyperelastic material are outlined; and examples are presented in illustration of Truesdell’s problem concerning analytical restrictions imposed on constitutive equations. Universal relations valid for all compressible and incompressible, isotropic materials are discussed. Some examples of non-uniqueness, including that of a neo-Hookean cube subject to uniform loads over its faces, are described. Elastic stability criteria and their connection with uniqueness in the theory of small deformations superimposed on large deformations are introduced, and a few applications are mentioned. Some previously unpublished results are presented throughout.

On Bayesian model selection for INGARCH models viatrans-dimensional Markov chain Monte Carlo methods

2021 ◽  
pp. 1471082X2110347
Author(s):  
Panagiota Tsamtsakiri ◽  
Dimitris Karlis
Keyword(s):  
Time Series ◽  
Model Selection ◽  
Bayesian Model ◽  
Linear Models ◽  
Simulation Experiment ◽  
Mean Values ◽  
The Past ◽  
Competing Models ◽  
Selection For ◽  
Log Linear

There is an increasing interest in models for discrete valued time series. Among them, the integer autoregressive conditional heteroscedastic (INGARCH) is a model that has found several applications. In the present article, we study the problem of model selection for this family of models. Namely we consider that an observation conditional on the past follows a Poisson distribution where its mean depends on its past mean values and on past observations. We consider both linear and log-linear models. Our purpose is to select the most appropriate order of such models, using a trans-dimensional Bayesian approach that allows jumps between competing models. A small simulation experiment supports the usage of the method. We apply the methodology to real datasets to illustrate the potential of the approach.

scholarly journals Uncertainty quantification of elastic material responses: testing, stochastic calibration and Bayesian model selection

2019 ◽  
Vol 1 (1) ◽  
Author(s):  
Danielle Fitt ◽  
Hayley Wyatt ◽  
Thomas E. Woolley ◽  
L. Angela Mihai
Keyword(s):  
Model Selection ◽  
Bayesian Model ◽  
Finite Elasticity ◽  
Tensile Tests ◽  
Bayesian Model Selection ◽  
Probability Density Functions ◽  
Uniaxial Tensile ◽  
Density Functions ◽  
Material Behaviour ◽  
Independent Probability

AbstractMotivated by the need to quantify uncertainties in the mechanical behaviour of solid materials, we perform simple uniaxial tensile tests on a manufactured rubber-like material that provide critical information regarding the variability in the constitutive responses between different specimens. Based on the experimental data, we construct stochastic homogeneous hyperelastic models where the parameters are described by spatially independent probability density functions at a macroscopic level. As more than one parametrised model is capable of capturing the observed material behaviour, we apply Baye theorem to select the model that is most likely to reproduce the data. Our analysis is fully tractable mathematically and builds directly on knowledge from deterministic finite elasticity. The proposed stochastic calibration and Bayesian model selection are generally applicable to more complex tests and materials.

scholarly journals Modal-based vibrothermography using feature extraction with application to composite materials

2019 ◽  
Vol 19 (4) ◽  
pp. 967-986 ◽  
Author(s):  
Xintian Chi ◽  
Dario Di Maio ◽  
Nicholas AJ Lieven
Keyword(s):  
Feature Extraction ◽  
Composite Materials ◽  
Damage Detection ◽  
Infrared Camera ◽  
Experimental Tests ◽  
Detection Algorithm ◽  
Modal Testing ◽  
Theoretical Development ◽  
Operational Environment ◽  
Practical Applications

This research focuses on the development of a damage detection algorithm based on modal testing, vibrothermography, and feature extraction. The theoretical development of mathematical models is presented to illustrate the principles supporting the associated algorithms, through which the importance of the three components contributing to this approach is demonstrated. Experimental tests and analytical simulations have been performed in laboratory conditions to show that the proposed damage detection algorithm is able to detect, locate, and extract the features generated due to the presence of sub-surface damage in aerospace grade composite materials captured by an infrared camera. Through tests and analyses, the reliability and repeatability of this damage detection algorithm are verified. In the concluding observations of this article, suggestions are proposed for this algorithm’s practical applications in an operational environment.

Natural variability of surface porosity of wine cork stoppers of different commercial classes

OENO One ◽  
2012 ◽  
Vol 46 (4) ◽  
pp. 331 ◽  
Author(s):  
Vanda Oliveira ◽  
Sofia Knapic ◽  
Helena Pereira
Keyword(s):  
Lateral Surface ◽  
Surface Porosity ◽  
Intrinsic Variability ◽  
Mean Values ◽  
Porosity Coefficient ◽  
Performance Development ◽  
And Performance ◽  
Definition Of ◽  
Cork Industry ◽  
Cork Stoppers

<p style="text-align: justify;"><strong>Aim</strong>: The aim of this study was to characterize the variability and to quantify the surface porosity of wine cork stoppers of different quality classes.</p><p style="text-align: justify;"><strong>Methods and results</strong> : The porosity of 300 cork stoppers was characterized by image analysis on the lateral surface and tops. Porosity coefficient was 2.4%, 4.0% and 5.5% for premium, good and standard stoppers, respectively. The lateral surface of stoppers was heterogeneous with respect to porosity features: the tangential regions presented higher porosity while the radial regions had larger pores.</p><p style="text-align: justify;"><strong>Conclusion</strong> : The quality classes of cork stoppers can be differentiated by the mean values of the main porosity features of their surface. There is a natural heterogeneity of the porosity features over the external surface of cork stoppers that can be traced back to the biological basis of cork formation and the production process.</p><p style="text-align: justify;"><strong>Significance and impact of the study</strong>: Natural cork stoppers are the premium product of the cork industry, with worldwide recognition of quality and performance as wine sealant. Due to the large sampling and detailed observation, the results presented in this study may be used for reinforcing quality requirements, e.g., with definition of standards to improve the classification system. A better understanding of cork intrinsic variability and of the anisotropy of porosity features shown by cork stoppers is important for performance development.</p>

The characteristics of coaxial and non-coaxial strain paths

1966 ◽  
Vol 1 (3) ◽  
pp. 216-222 ◽  
Author(s):  
T. C. Hsu
Keyword(s):  
Strain Path ◽  
Total Strain ◽  
Large Strains ◽  
Manufacturing Processes ◽  
Practical Applications ◽  
Principal Axes ◽  
Strain Paths

In manufacturing processes involving large strains, the properties of the material undergoing deformation depend not only on the current total strain but on the previous strain path as well. Strain paths are divided into two major types, those in which the principal axes of strain remain fixed with respect to the material (coaxial strain paths), and those in which they rotate (non-coaxial strain paths). The characteristics of the two types of strain path are explained. Particular types of non-coaxial strain path related to practical applications are discussed in further detail and examples based on actual measurements are given.

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